# Lucy is a dress maker. She sews 4/7 of a dress in 3/4 hour. At this rate, how many dresses does Lucy sew in one hour?

Dec 30, 2016

$\frac{16}{21} \text{ dresses}$

#### Explanation:

The ratio of time required to dresses made is
color(white)("XXX")3/4* k " hours" : 4/7 * k " dresses" for any constant $k$

Specifically, if we want $1 \text{ hour}$ then $k$ will need to be $\textcolor{g r e e n}{\frac{4}{3}}$.

So $\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{3}}}}{\textcolor{b l u e}{\cancel{\textcolor{b l a c k}{4}}}} \times \frac{\textcolor{b l u e}{\cancel{\textcolor{g r e e n}{4}}}}{\textcolor{red}{\cancel{\textcolor{g r e e n}{3}}}} \text{ hours" : 4/7 xx color(green)(4/3) " dresses}$

$\Rightarrow 1 \text{ hour" : 16/21 "dresses}$